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The stability of oscillatory internal waves

Published online by Cambridge University Press:  28 March 2006

Russ E. Davis  and
Andreas Acrivos
Russ E. Davis
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford, California Present address: Institute of Geophysics and Planetary Physics, University of California, La Jolla, California.
Andreas Acrivos
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford, California
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Abstract

The stability of a periodic internal wave has been investigated experimentally and theoretically. From the analysis it is found that if a primary wave, with wave-number k0 and frequency ω0, is perturbed by two infinitesimal wave-like disturbances with wave-numbers k1 and k1 + k0 and frequencies ω1 and ω1 + ω0, exponential growth of these disturbances will take place under certain conditions. The analysis also indicates which resonantly interacting disturbances can induce an instability and, when viscous dissipation is accounted for, predicts the minimum amplitude for which a wave is unstable. Experimental results demonstrate that this type of instability can cause the breakdown of a first mode internal wave propagating in a fluid composed of two layers of uniform density separated by a thin region in which the density varies continuously.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 30 , Issue 4 , 22 December 1967 , pp. 723 - 736
Copyright
© 1967 Cambridge University Press

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